When Multiplication Answers are Smaller

This activity addresses concerns raised when students encounter a product of multiplication of rational numbers, that is smaller than either of the factors. The question they ask is why is the answer smaller when we're multiplying?

Step 1: Review the definition for multiplication.Multiplication describes when you combine equal groups of things.
Step 2: Ask, What do we know about multiplication? Examples:

• It's repeated addition.
• The answer is always bigger.
• Used most often when counting things like money, shopping, or ordering things.

These above examples are not always true. The following are true:

• You can illustrate multiplication using an array.
• The answer is not always larger than the two factors.
• Multiplication is often a more efficient way to combine things together.

Step 3: Multiplication answers the question, "What is _ groups of _ ?"� For example, "3 groups of 4 pencil is 12 pencils", or "2 groups of 2 students is 4 students."
Step 4:� When we multiply fractions we are asking the same question.� "1/2 of 4 candies is 2 candies"
Step 5:� Create you own examples using fractions.
Step 6:� Refer to the Rectangular Multiplication of Fractions applet for representations of multiplying fractions.